Hello,
It's from Innopolis Open, Final Round, 2015-2016, the problem A. I can't approach it, can somebody give me a hint?
Have nice day,
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When the left end of the segment (segment of length L) moves between coordinate x0 and x0 + 1 (x0 is integer), the covered area changes as a linear function. The sum/difference of slopes is enough to say how it changes.
You should sweep over the given points, updating something when the sweep is over some point or some point is L to the right from the sweep line. This way you will know the area for any placement you want.